Multi-level modulation, such as the modulation produced by trellis encoders, is a well-known technique for improving the performance of a data transmission and reception system. For example, multi-level modulation results in an improvement in the signal-to-noise (S/N) performance of the data transmission and reception system at a given power level. Alternatively, multi-level modulation permits the transmitted power level required to achieve a given signal-to-noise performance to be reduced.
In essence, trellis-coded modulation (TCM) comprises the use of a multi-state convolution encoder to convert each k input data bits of an input sequence of data bits into k+n output data bits, and is therefore referred to as a rate k/(k+n) convolution encoder. The output bits are then mapped into a sequence of discrete multi-level symbols of a modulated carrier for data transmission. Each multi-level symbol typically has one of 2.sup.(k+n) values. These values can be phase and/or amplitude values. By coding the input data bits in a state-dependent sequential manner, increased minimum Euclidean distances between the allowable transmitted sequences may be achieved leading to a reduced error probability where a maximum likelihood decoder (for example, a Viterbi decoder) is used in the receiver.
In an example of a data transmission and reception system which uses multi-level modulation, successive pairs of data bits X.sub.1, X.sub.2 are encoded for transmission as eight-level, one-dimensional symbols. More specifically, bit X.sub.1 is convolutionally encoded using a four-state convolution encoder to generate bits Z.sub.0, Z.sub.1, and bit X.sub.2 is precoded to generate bit Z.sub.2. Bits Z.sub.2, Z.sub.1, and Z.sub.0 are mapped to respective eight-level symbols using a one-dimensional symbol constellation. As an example, 2.sup.(k+n) amplitude values of -7, -5, -3, -1, +1, +3, +5, and +7 may be used for the one-dimensional symbol constellation. The eight-level symbols, after insertion of appropriate sync signals, are transmitted in the form of a suppressed carrier vestigial sideband (VSB) signal.
This signal is received by a receiver which, at the front end, may include a tuner, an IF demodulator, an analog-to-digital (A/D) converter, a channel equalizer, and a decoder. The decoder decodes the multi-level symbols in order to recover the successive pairs of data bits X.sub.1, X.sub.2. The receiver may also include a phase tracker to reduce phase noise errors and amplitude-related errors. That is, many signal receivers, such as television receivers, which are used in data transmission and reception systems and which are designed for receiving suppressed carrier VSB signals, use a double conversion tuner at the receiver front end. The first local oscillator of such a tuner typically exhibits a relatively high level of phase noise in the demodulated data. In addition, the demodulated data may be degraded by amplitude-related errors resulting in the demodulated data being recovered with undesired offsets and/or at undesired levels of gain. These phase noise errors and amplitude-related errors may lead to an unacceptable error rate if uncorrected, especially in the case of tightly packed data constellations. In order to minimize the error rate due to phase noise errors and amplitude-related errors, the multi-level symbols may be processed by a phase tracker. An example of such a phase tracker is disclosed in U.S. Pat. No. 5,406,587.
Circuits, such as equalizers and phase trackers, usually compute a sliced data signal from a continuous valued signal. The conventional slicer slices the eight-level symbols in accordance with a set of seven slice levels to produce one of eight quantized output values. While this approach to slicing is perfectly satisfactory in theory, performance of the conventional slicer is usually degraded under noisy conditions which cause the amplitude of a multi-level symbol level to cross a slice level solely due to noise acquired during transmission and reception.
For example, the amplitude of a symbol originally having a value of +5 (using the -7, -5, -3, -1, +1, +3, +5, +7 constellation described above) may be degraded by noise such that its value at the output of the phase tracker may be +6.1. Accordingly, a slicing system, which slices the received signal at -6, -4, -2, 0, +2, +4, and +6 will produce an incorrect quantized value of +7 rather than the proper quantized value of +5 for use by the phase tracker.
The present invention solves one or more of the above described problems.